1) Given parametric equations x(t) = 2 + t and y(t) = 2-1, determine the rectangular...
Determine the equation of the given graph of the ellipse: у (-2,8) (-2,5+15) - (-4,5) (0,5) (-2,5): (-2,5-15) - (-2, 2) +
A pair of parametric equations is given. x = y=t+3 (a) Sketch the curve represented by the parametric equations. -10 5 -10 5 10 -10 -51 5 10 * -10 -5 MM 5 10 (b) Find a rectangular-coordinate equation for the curve by eliminating the parameter.
Convert the parametric equations x = t2 + 1, y = 1 - t to rectangular form.
2) Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t).y = 2 cos(t);0 st <270 (b) x2 + y2 = 2 c) x2 + y2 = 4 (d) y = x2 - 4 (a) y2 - x2 = 2 (e) y = x2 - 2
Find a set of parametric equations to represent the graph of the rectangular equation y = 2 - x2 using t = x + 1
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
Consider the following parametric equations. x = √1 + 2 , y = 2√t; 0 ≤ t ≤ 16 a. Eliminate the parameter to obtain an equation in x and y. b. Describe the curve and indicate the positive orientation.
4. Find a rectangular equation for the plane curve defined by the parametric equations x=3sin()y = 3 cos(1) (a) y = x-3 (C) y = 7-9 (b) x + y = 9 (d) x+y = 3 5. Write the equation r = 4 cos in rectangular form. (a) x + y - 4y (b) x² + y = 4x (C) (x + y) = 4x (d) (x+y)* = 4y 6. Write [2(cos 15° + i sin 15°)] in rectangular form....
Consider the parametric equations below. x = 2 + 4t y = 1-t2 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.(b) Eliminate the parameter to find a Cartesian equation of the curve. y = _______ Consider the parametric equations below. x = 3t - 5 y = 2t + 4 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...
7. Use the given information about the parametric equations x-ft) and y-g(t) to graph the Cartesian (rectangular) x-y relation. ft) is the absolute value of a linear function, and three points on the graph of this function are: H0, x=1; t-1, x 0; and t=2, x=1 g(t) is a linear function, and two points on the graph of y-g(t) aret-0, y=1; and t-1. y-0.